Package edu.jas.gb
Class WordReductionAbstract<C extends RingElem<C>>
java.lang.Object
edu.jas.gb.WordReductionAbstract<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
WordReduction<C>
,Serializable
- Direct Known Subclasses:
WordPseudoReductionSeq
,WordReductionSeq
public abstract class WordReductionAbstract<C extends RingElem<C>>
extends Object
implements WordReduction<C>
Polynomial word reduction abstract class. Implements common S-Polynomial,
normalform, module criterion and irreducible set.
- See Also:
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Field Summary
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionirreducibleSet
(List<GenWordPolynomial<C>> Pp) Irreducible set.boolean
isNormalform
(List<GenWordPolynomial<C>> Pp) Is in Normalform.boolean
isNormalform
(List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap) Is in Normalform.boolean
isReducible
(List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap) Is reducible.boolean
isReductionNF
(List<GenWordPolynomial<C>> lrow, List<GenWordPolynomial<C>> rrow, List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap, GenWordPolynomial<C> Np) Is reduction of normal form.boolean
isTopReducible
(List<GenWordPolynomial<C>> P, GenWordPolynomial<C> A) Is top reducible.normalform
(List<GenWordPolynomial<C>> Pp, List<GenWordPolynomial<C>> Ap) Normalform Set.SPolynomial
(C a, Word l1, GenWordPolynomial<C> A, Word r1, C b, Word l2, GenWordPolynomial<C> B, Word r2) S-Polynomials of non-commutative polynomials.SPolynomial
(Overlap ol, C a, GenWordPolynomial<C> A, C b, GenWordPolynomial<C> B) S-Polynomials of non-commutative polynomials.SPolynomials
(GenWordPolynomial<C> Ap, GenWordPolynomial<C> Bp) S-Polynomials of non-commutative polynomials.Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface edu.jas.gb.WordReduction
leftNormalform, leftNormalform, normalform, normalform, rightNormalform, rightNormalform
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger
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Constructor Details
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WordReductionAbstract
public WordReductionAbstract()Constructor.
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Method Details
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SPolynomials
S-Polynomials of non-commutative polynomials.- Specified by:
SPolynomials
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
Ap
- word polynomial.Bp
- word polynomial.- Returns:
- list of all spol(Ap,Bp) the S-polynomials of Ap and Bp.
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SPolynomial
public GenWordPolynomial<C> SPolynomial(C a, Word l1, GenWordPolynomial<C> A, Word r1, C b, Word l2, GenWordPolynomial<C> B, Word r2) S-Polynomials of non-commutative polynomials.- Specified by:
SPolynomial
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
a
- leading base coefficient of B.l1
- word.A
- word polynomial.r1
- word.b
- leading base coefficient of A.l2
- word.B
- word polynomial.r2
- word.- Returns:
- list of all spol(Ap,Bp) the S-polynomials of Ap and Bp.
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SPolynomial
public GenWordPolynomial<C> SPolynomial(Overlap ol, C a, GenWordPolynomial<C> A, C b, GenWordPolynomial<C> B) S-Polynomials of non-commutative polynomials.- Parameters:
ol
- Overlap tuple.a
- leading base coefficient of B.A
- word polynomial.b
- leading base coefficient of A.B
- word polynomial.- Returns:
- list of all spol(Ap,Bp) the S-polynomials of Ap and Bp.
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normalform
public List<GenWordPolynomial<C>> normalform(List<GenWordPolynomial<C>> Pp, List<GenWordPolynomial<C>> Ap) Normalform Set.- Specified by:
normalform
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial list.- Returns:
- list of nf(a) with respect to Pp for all a in Ap.
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isTopReducible
Is top reducible.- Specified by:
isTopReducible
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
P
- polynomial list.A
- polynomial.- Returns:
- true if A is top reducible with respect to P.
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isReducible
Is reducible.- Specified by:
isReducible
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- true if Ap is reducible with respect to Pp.
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isNormalform
Is in Normalform.- Specified by:
isNormalform
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- true if Ap is in normalform with respect to Pp.
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isNormalform
Is in Normalform.- Specified by:
isNormalform
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.- Returns:
- true if each Ap in Pp is in normalform with respect to Pp\{Ap}.
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irreducibleSet
Irreducible set.- Specified by:
irreducibleSet
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.- Returns:
- a list P of monic polynomials which are in normalform wrt. P and with ideal(Pp) = ideal(P).
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isReductionNF
public boolean isReductionNF(List<GenWordPolynomial<C>> lrow, List<GenWordPolynomial<C>> rrow, List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap, GenWordPolynomial<C> Np) Is reduction of normal form.- Specified by:
isReductionNF
in interfaceWordReduction<C extends RingElem<C>>
- Parameters:
lrow
- left recording matrix.rrow
- right recording matrix.Pp
- a polynomial list for reduction.Ap
- a polynomial.Np
- nf(Pp,Ap), a normal form of Ap wrt. Pp.- Returns:
- true, if Np + sum( row[i]*Pp[i] ) == Ap, else false.
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